The density of a fluid, denoted by ρ, is its mass per unit volume. Density is highly variable in gases and increases nearly proportionally to the pressure level. Density in liquids is nearly constant; the density of water (about 1000 kg/m3) increases only 1 percent if the pressure is increased by a factor of 220. Thus most liquid flows are treated analytically as nearly "incompressible."
In general, liquids are about three orders of magnitude more dense than gases at atmospheric pressure. The heaviest common liquid is mercury, and the lightest gas is hydrogen. The physical parameters in various liquid and gas flows might vary considerably. The differences are often resolved by the use of dimensional analysis.
The masses of samples do not change if the temperature is raised or lowered. However, the volumes of solids and of most liquids increase slightly if the temperature is raised. The volumes of all gases held at constant pressure increase greatly when temperature is raised. If the denominator of a fraction is increased while the numerator remains constant, the value of the fraction decreases. Density usually decreases with increasing temperature. When the density of a material is given, the temperature at which the density was measured should also be given.
The SI unit for density, kg/m3, is derived from the base units for mass and length.
The specific volume of a substance is defined as the volume per unit mass. Typically specific volume uses the symbol v. The density of a substance is defined as the mass per unit volume, and it is therefore the reciprocal of the specific volume. Density is designated by the symbol ρ. Specific volume and density are intensive properties.
The specific volume of a system in a gravitational field may vary from point to point. For example, if the atmosphere is considered a system, the specific volume increases as the elevation increases. Therefore, the definition of specific volume involves the specific volume of a substance at a point in a system.
These two quantities can also be expressed in molal terms. A bar over either symbol may be to indicate that the quantity is a molal quantity. For example, molal density may be represented by the symbol:
ρ
and would be expressed in kmol/m3. Similarly, molal specific density may be represented by the symbol:
v
and would be expressed in m3/kmol.
Density is defined as mass per unit volume. The reciprocal of density is the specific volume v, which is defined as volume per unit mass. That is, v = V/m = 1/ρ. For a differential volume element of mass δm and volume δV, density can be expressed as ρ = δm/δV.
The density of a substance, in general, depends on temperature and pressure. The density of most gases is proportional to pressure and inversely proportional to temperature. Liquids and solids, on the other hand, are essentially incompressible substances, and the variation of their density with pressure is usually negligible. At 20°C, for example, the density of water changes from 998 kg/m3 at 1 atm to 1003 kg/m3 at 100 atm, a change of just 0.5 percent. The density of liquids and solids depends more strongly on temperature than it does on pressure. At 1 atm, for example, the density of water changes from 998 kg/m3 at 20°C to 975 kg/m3 at 75°C, a change of 2.3 percent, which can still be neglected in many engineering analyses.